Isobaric single charge-exchange reactions, changing nuclear charges by one unit but leaving the mass partitions unaffected, have been for the first time investigated by peripheral collisions of $^{112}$Sn ions accelerated up to 1textit{A} GeV at the GSI facilities. The high-resolving power of the FRS spectrometer allows us to obtain $(p, n)$-type isobaric charge-exchange cross sections with an uncertainty of $3.5%$ and to separate quasi-elastic and inelastic components in the missing-energy spectra of the ejectiles. The inelastic component is associated to the excitation of the $Delta$(1232) isobar resonance and the emission of pions in s-wave both in the target and projectile nucleus, while the quasi-elastic contribution is associated to the nuclear spin-isospin response of nucleon-hole excitations. An apparent shift of the $Delta$-resonance peak of $sim$63 MeV is observed when comparing the missing-energy spectra obtained from the measurements with proton and carbon targets. A detailed analysis, performed with a theoretical model for the reactions, indicates that this observation can be simply interpreted as a change in the relative magnitude between the contribution of the excitation of the resonance in the target and in the projectile.
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